Question

A body is at rest at $x=0$. At $t=0$, it starts moving in the positive $x$ -direction with a constant acceleration. At the same instant another body passes through $x=0$ moving in the positive $x$ - direction with a constant speed. The position of the first body is given by $x_1(t)$ after 't' and that of the second body by $x_2(t)$ after the same time interval. Which of the following graphs correctly describes $\left(x_1-x_2\right)$ as a function of time 't'?

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

At $t=0$ the first body starts moving with constant acceleration while the second body is already moving with certain constant speed. So the distance covered by the first body $x$, is smaller that covered by the second body $x_2$, i.e., $x_1<x_2$ or $x_1-x_2=$ negative till the first body attains the speed equal to that of second body. At that instant $x_1=x_2$ or $x_1-x_2=0$ and after that $x_1>x_2$ i.e. $-x_2=$ positive and goes on increasing with increasing